scholarly journals Global threshold dynamics of an SVIR model with age-dependent infection and relapse

2016 ◽  
Vol 11 (sup2) ◽  
pp. 427-454 ◽  
Author(s):  
Jinliang Wang ◽  
Jiying Lang ◽  
Yuming Chen
Keyword(s):  
Threshold Dynamics ◽  
Global Threshold ◽  
Age Dependent

Global threshold dynamics of an age structured alcoholism model

2021 ◽  
pp. 2150013
Author(s):  
Soufiane Bentout ◽  
Salih Djilali ◽  
Abdenasser Chekroun
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Global Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Threshold ◽  
Age Structured ◽  
The Basic Reproduction Number ◽  
Proper Strategy

We consider in this research an age-structured alcoholism model. The global behavior of the model is investigated. It is proved that the system has a threshold dynamics in terms of the basic reproduction number (BRN), where we obtained that alcohol-free equilibrium (AFE) is globally asymptotically stable (GAS) in the case [Formula: see text], but for [Formula: see text] we found that the system persists and the nontrivial equilibrium (EE) is GAS. Furthermore, the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated, which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations. The obtained mathematical results are tested numerically next to its biological relevance.

scholarly journals Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Junyuan Yang ◽  
Xiaoyan Wang
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Age Dependent ◽  
The Basic Reproduction Number

We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate.

Global threshold dynamics of SIQS epidemic model in time fluctuating environment

2017 ◽  
Vol 10 (04) ◽  
pp. 1750060 ◽  
Author(s):  
Shang Li ◽  
Meng Fan ◽  
Xinmiao Rong
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Integral Operator ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Global Threshold ◽  
Linear Integral ◽  
Disease Free ◽  
The Basic Reproduction Number

The paper characterizes the global threshold dynamics of an epidemic model of SIQS type in environments with fluctuations, where the quarantine class is explicitly involved. Criteria are established for the permanence and extinction of the infective in environments with time oscillations. In particular, we further consider an environment which varies periodically in time. The global threshold dynamic scenarios i.e. the existence and global asymptotic stability of the disease-free periodic solution, the existence of the endemic periodic solution and the permanence of the infective are completely characterized by the basic reproduction number defined by the spectral radius of an associated linear integral operator.

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